A lead ball, with an initial temperature of 25.0oC, is released from a height of 119.0 m. It does not bounce when it hits a hard surface. Assume all the energy of the fall goes into heating the lead. Find the temperature (in degrees C) of the ball after it hits. Data: clead = 128 J/kgoC.
To find the temperature of the lead ball after it hits the surface, we need to use the principle of conservation of energy. The potential energy of the ball at the height is converted into thermal energy, which will increase the temperature of the ball.
The potential energy (PE) can be calculated using the formula:
PE = mgh
where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the fall.
The mass of the lead ball is not given, so we cannot directly calculate the potential energy. However, we can assume that the mass cancels out when the energy is converted entirely into heating the lead.
Since all the energy goes into heating the lead ball, we can write the equation:
PE = mgh = mcΔT
where c is the specific heat capacity of lead and ΔT is the change in temperature.
Rearranging the equation, we get:
ΔT = (mgh) / (mc)
Since m cancels out, we are left with:
ΔT = (gh) / c
Now, we can plug in the given values to calculate the change in temperature:
g = 9.8 m/s^2 (acceleration due to gravity)
h = 119.0 m (height of the fall)
c = 128 J/kg⋅°C (specific heat capacity of lead)
ΔT = (9.8 m/s^2 * 119.0 m) / (128 J/kg⋅°C)
ΔT = 9.074 °C
Finally, to find the temperature of the ball after it hits, we add the change in temperature to the initial temperature:
Temperature after hitting = Initial temperature + ΔT
Temperature after hitting = 25.0 °C + 9.074 °C
Temperature after hitting ≈ 34.074 °C
Therefore, the temperature of the lead ball after it hits the surface is approximately 34.074 °C.